This is a really good saying, I'll break it down for you. "Stay Hungry" this doesn't mean to literally be hungry, and not eat food, this is stay hungry as in 'eager'. It's basically saying that you should never be satisfied with a result, you should always keep going for more because you're 'hungry' for more (Metaphorically, not literally) "Stay foolish" this doesn't mean to literally be foolish either, it means that you should always push yourself to do things that people say you can't. Normally if you try to do something that is impossible, someone would call you a 'fool', or someone who acts without wisdom. This saying basically means "Don't ever accept a result, push yourself beyond your limits and do that which people tell you is impossible"

Stay hungry, stay foolish means to always keep wanting. To be foolish means to accept that you will make mistakes. When you are overly wise (in this case), you could be too cautious and not step into the unknown.